Answer :

Let's solve the inequality step by step:

We are given:
[tex]\[
-17c - 18 - 18 > -9c + 20
\][/tex]

1. Simplify both sides of the inequality:

On the left side, simplify:
[tex]\[
-17c - 18 - 18 = -17c - 36
\][/tex]

On the right side, it remains:
[tex]\[
-9c + 20
\][/tex]

So, the inequality becomes:
[tex]\[
-17c - 36 > -9c + 20
\][/tex]

2. Get all terms involving [tex]\(c\)[/tex] on one side:

Add [tex]\(17c\)[/tex] to both sides:
[tex]\[
-36 > 8c + 20
\][/tex]

3. Isolate the [tex]\(c\)[/tex] term:

Subtract 20 from both sides:
[tex]\[
-56 > 8c
\][/tex]

4. Solve for [tex]\(c\)[/tex]:

Divide by 8:
[tex]\[
-\frac{56}{8} > c
\][/tex]

Simplify:
[tex]\[
-7 > c
\][/tex]

This can be rewritten with [tex]\(c\)[/tex] on the left side:
[tex]\[
c < -7
\][/tex]

The interval solution for this inequality is:
[tex]\[
c < -7
\][/tex]

This means [tex]\(c\)[/tex] can be any number less than [tex]\(-7\)[/tex].

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Rewritten by : Barada